Question: Simplify the following expression and state the condition under which the simplification is valid: $x = \dfrac{p^2 + 9p + 14}{p^2 + 7p}$
Solution: First factor the expressions in the numerator and denominator. $ \dfrac{p^2 + 9p + 14}{p^2 + 7p} = \dfrac{(p + 2)(p + 7)}{(p)(p + 7)} $ Notice that the term $(p + 7)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(p + 7)$ gives: $x = \dfrac{p + 2}{p}$ Since we divided by $(p + 7)$, $p \neq -7$. $x = \dfrac{p + 2}{p}; \space p \neq -7$